solution_quiz3

# solution_quiz3 - Problem 1 Solution(a 29 29 29 32 2 1 1 3 3...

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Unformatted text preview: Problem 1 Solution: (a) ( 29 ( 29 ( 29 ) ( ) ( 32 . 2 . 1 1 3 3 1 32 . 2 . 1 1 2 1 1 2 1 32 . 2 . 1 1 1 ) ( 2 1 3 2 1 2 1 2 1 1 2 1 2 1 1 z X z Y z z z z z z z z z z z z z z z z H =-- + + + =-- + + + = + + -- + =--------------- So the difference equation is ] 3 [ ] 2 [ 3 ] 1 [ 3 ] [ ] 2 [ 32 . ] 1 [ 2 . 1 ] [- +- +- + =---- n x n x n x n x n y n y n y (b) The transfer function is 2 1 3 2 1 32 . 2 . 1 1 3 3 1 ) (------- + + + = z z z z z z H (c) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 22 . 42 . 1 1 ) 17 2 . 6 . ( 1 ) 17 2 . 6 . ( 1 1 32 . 2 . 1 1 1 1 32 . 2 . 1 1 1 1 32 . 2 . 1 1 2 1 1 ) ( 3 1 1 3 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 +- + =-- +- + =-- + + =-- + + =-- + + + =---------------- z z z z z z z z z z z z z z z z z z z z z H So the zeros: -1 (3-order) The poles: 1.42, -0.22, 0 (d) 1 1 1 2 1 1 1 2 1 3 2 1 22 . 1 6302 . 5 42 . 1 1 2864 . 4 3438 . 2 125 . 3 32 . 2 . 1 1 3438 . 1 938 . 8 3438 . 2 125 . 3 32 . 2 . 1 1 3 3 1 ) (----------...
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solution_quiz3 - Problem 1 Solution(a 29 29 29 32 2 1 1 3 3...

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